Difference between revisions of "Power rule"
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| − | + | The power rule allows one to calculate the derivative of a power of a function in terms of the derivative of the function itself. The power rule states that | |
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| + | <math> \frac{d}{dx} (x^n) = nx^{n-1} </math> | ||
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| + | for all integers <math> n </math>. This rule is useful when combined with the [[chain rule]]. As an example we can compute the derivative of <math> f(x) = (\sin(x))^n</math> as | ||
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| + | <math> f'(x) = \frac{d}{dx} (\sin(x))^n = n(\sin(x))^{n-1}\cos(x) </math> | ||
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| + | [[Category:Mathematics]] | ||
Revision as of 22:25, May 3, 2010
The power rule allows one to calculate the derivative of a power of a function in terms of the derivative of the function itself. The power rule states that
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx} (x^n) = nx^{n-1} }
for all integers Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n } . This rule is useful when combined with the chain rule. As an example we can compute the derivative of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = (\sin(x))^n} as
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f'(x) = \frac{d}{dx} (\sin(x))^n = n(\sin(x))^{n-1}\cos(x) }